1. Field of the Invention
The present invention relates to a voltage controlled oscillator (VCO). More specifically, the present invention relates to a VCO that includes a ring oscillator that exhibits an improved (reduced) gain.
2. Related Art
Voltage controlled oscillator (VCO) circuits are typically used to create frequency modulated (FM) signals. That is, a VCO circuit provides an output signal having a frequency (fOUT) that varies in response to changes in an input supply voltage (VIN). VCO circuits are the main building block for frequency modulation (FM) circuits and phase locked loop (PLL) circuits.
The gain (KVCO) of a VCO circuit can be described mathematically as, KVCO=ΔfOUT/ΔVIN, where ΔfOUT represents the change in the output frequency and ΔVIN represents the change in the input voltage. To obtain a desired modulation index, the gain of a VCO circuit should be appropriately low. However, the gain of a conventional VCO is typically too high to allow a frequency modulation system to be built using only a VCO circuit. Instead, frequency modulation systems are typically constructed using a low-frequency VCO circuit and one or more multiplier circuits. The output signal provided by the low-frequency VCO circuit is multiplied to obtain the desired high frequency output signal.
A ring oscillator is an inexpensive type of VCO circuit that typically has a large gain that is proportional to the frequency of operation. This causes two problems: (1) it is very difficult to achieve wide bandwidth frequency modulation with a reasonable input voltage, and (2) for a certain frequency modulation index, a small signal may be needed at the input, thereby reducing the signal-to-noise ratio, resulting in undesirable phase noise.
FIG. 1 is a block diagram of a conventional ring oscillator circuit 100. Ring oscillator 100 includes an odd number of identical inverting amplifier stages 101-102N+1. In the described examples, the odd number of stages is represented by the value (2N+1), wherein N is an integer greater than or equal to 1. The frequency control input terminal of each amplifier stage is connected to receive a control voltage VIN from a common point P. Capacitor 20, which has a capacitance Cf, implements noise filtering of the control voltage VIN. Ring oscillator 100 draws a total current IP, which is equal to the sum of the currents IN through each of the 2N+1 inverting amplifier stages.
FIG. 2 is a circuit diagram illustrating conventional inverting amplifier stages 101 and 102, which are implemented by CMOS inverters that include PMOS transistors 201-202 and NMOS transistors 203-204. The current consumption of each of the inverting amplifier stages 101-102N+1 can be represented by the following equation,IN=C*f*VIN  (1)wherein ‘C’ represents the total node capacitance between two of the CMOS inverters (i.e., the sum of the PMOS and NMOS gate and drain capacitances), ‘f’ represents the frequency of the output signal provided by each of the inverting amplifier stages, and VIN represents the voltage swing of the output signal provided by each of the inverting amplifier stages.
Within each CMOS amplifying inverter stage, the PMOS transistor (e.g., PMOS transistor 201) is typically designed to have the same threshold voltage (VT) and the same β value as the associated NMOS transistor (e.g., NMOS transistor 203). Note that the β value of a transistor is defined as μ*COX*W/L, wherein μ is the mobility of the transistor, COX is the gate capacitance of the transistor, W is the width of the transistor, and L is the length of the transistor. In this case, the current consumption (IN) of each CMOS amplifying inverter stage can also be represented by the following equation.IN=β*(0.5*VIN−VT)2  (2)
Note that Equation (2) assumes that transitions in each inverting amplifier stage occur while the associated PMOS and NMOS transistors operate in a saturation condition, such that Equation (2) represents an approximation of transistor drain current. Equation (2) further relies on the fact that each transition occurs around ½ the input voltage VIN.
Because there are 2N+1 identical CMOS inverters operating in an identical manner, the total current (IP) drawn by ring oscillator circuit 100 is equal to the sum of the currents of the inverting amplifier stages. This relationship can be represented by the following equation.IP=(2N+1)*IN  (3)
Combining Equations (1) and (3) results in the following equation.IP=(2N+1)*(C*f*VIN)  (4)
Similarly, combining Equations (2) and (3) results in the following equation.IP=(2N+1)*β*(0.5*VIN−VT)2  (5)
Taking the partial derivative of Equation (4) with respect to the input voltage VIN yields the following equations.∂IP/∂VIN=∂/∂VIN((2N+1)*C*f*VIN)  (6)
Because only the frequency f and the input voltage VIN vary with respect to changes in the input voltage VIN, Equation (6) can be simplified as follows.∂IP/∂VIN=(2N+1)*C*VIN*∂f/∂VIN+(2N+1)*C*f*∂VIN/∂VIN  (7)∂IP/∂VIN=(2N+1)*C*VIN*∂f/∂VIN+(2N+1)*C*f  (8)
Similarly, taking the partial derivative Equation (5) with respect to the input voltage VIN yields the following equations.∂IP/∂VIN=∂/∂VIN((2N+1)*β*(0.5*VIN−VT)2)  (9)∂IP/∂VIN=(2N+1)*β*∂/∂VIN(0.25*VIN2−VIN*VT+VT2)  (10)∂IP/∂VIN=(2N+1)*β*(0.5*VIN−VT+0)  (11)∂IP/∂VIN=(2N+1)*β*(0.5*VIN−VT)  (12)
Combining Equations (8) and (12) results in the following equation.β*(0.5*VIN−VT)=C*VIN*∂f/∂VIN+C*f  (13)
Solving Equation (13) for ∂f/∂VIN results in the following equation, which represents the gain (K100) of ring oscillator 100.∂f/∂VIN=[β*(0.5*VIN−VT)−C*f]/(C*VIN)=K100  (14)
The gain K100 represented by Equation (14) is undesirably high for certain applications such as frequency modulation. This high gain results in the undesirable operating characteristics described above. It would therefore be desirable to have an improved ring oscillator circuit that exhibits a reduced gain with respect to ring oscillator 100. It would further be desirable if such an improved ring oscillator does not require the use of excessive additional circuitry.